Cancel half of shares before company's inexperienced new director starts (7)
I believe the answer is:
rescind
'cancel' is the definition.
(rescinding is a kind of cancelling)
'half of shares before company's inexperienced new director starts' is the wordplay.
'half of' indicates taking half.
'before' means one lot of letters go next to another.
'starts' indicates taking the first letters.
The initial letters of 'companys inexperienced new director' is 'cind'.
'shares' cut in half is 'res'.
'res'+'cind'='RESCIND'
(Other definitions for rescind that I've seen before include "Countermand" , "Revoke (order)" , "Cinders (anag.)" , "Set aside law" , "Discern in order to cancel, say a law" .)